Factor This!
This is the greatest common factor of
18x^3-12x^2+6x
What is 6x?
This polynomial, x^3-6x^2+x-6 , has this many real zeros and this many imaginary zeros.
What is 1 real zero and 2 imaginary zeros?
A polynomial function has this end behavior:
as x-> oo, f(x) -> +oo , and as
x->-oo, f(x) -> -oo . The degree must be this type (even or odd) and the leading coefficient must be this sign.
What is odd degree and positive leading coefficient?
When you subtract 3x^2-5x+7 from 8x^2+2x-4 , you get this polynomial.
What is 5x^2+7x-11 ?
A company sells 120 items at $400 eahc. For every $5 increase in prices, they sell 1 fewer item. This equation represents R(x) based on x price increases.
What is R(x)=(400+5x)(120-x) ?
This is the complete factorization of
x^2(3x-4)-(3x-4)
What is
(3x-4)(x-1)(x+1)?
These are all the zeros of the polynomial, y=2x^3-5x^2-14x+8
What are x=-2, 0.5, and 4?
The cost function c(x) is decreasing on the interval 150<x<300 . If you currently purchase 200 items, you should do this to save money.
What is purchase more items?
Two businesses charge 60+3x and 80 +20x dollars. When they merge and average their prices, this is the new pricing function p(x).
What is p(x)=70+25x ?
A box has volume 150 cubic cm. Its width is 3 times its heigh and its length is 4 more than 2 times its width. This equation can be used to solve for the height h.
What is 150=h(3h)(6h+4) ?
When you evaluate f(-2) for the function
f(x)=4x^4-7x^3+5x^2-3x , you get this value, which tells you whether (x+2) is a factor.
What is 150, and no (x+2) is not a factor because it does not equal 0?
A polynomial with all real coefficients has roots at -3 and 2-5i. This is the minimum degree of the polynomial.
What is 3 (or degree 3)?
A polynomial has x-intercepts at -3, 2, and 6. The graph touches the x-axis as x-2. With a leading coefficient of 1, this is the factorization of the polynomial.
What is f(x)=(x+3)(x-2)^2(x-6) ?
A company has revenue R(x) = 8000-5x^2 and expenses E(x)=30x+1200 . This polynomial represents their profit P(x).
What is P(x)=-5x^2-30x+6800 ?
A projectile's heigh is h(t)=-16t^2+32t+12 . A platform is at 20 feet. At these two times, the projectile reaches the platform height.
What is 0.5 and 1.5 seconds.
For the polynomial, h(x)=5x^3-2x^2+9x+m , when divided by (x-3), the remainder is 18. This is the value of m.
What is -108?
This polynomial function has zeros at -4 and 1, with a double root at 3. This is the factored form of the function.
What is f(x)=(x+4)(x-1)(x-3)^2 ?
A temperature table shows: at 0 min (5 degrees C), 10 min (8 degrees C), 20 min (11 degrees C), 30 min (9 degrees C), and 40 min (6 degrees C). The temperature is increasing during this time interval.
What is between 0 and 20 minutes?
When the polynomial p(x)=6x^3+11x^2-9x+14 is divided by (x+2), you get this remainder.
What is 28?
A ball's height follows h(t) = -16t² + 40t + 8, and a hoop is at g(t) = 16 feet. To the nearest hundredth, this is the time when the ball reaches the hoop as it falls.
A polynomial function has x-intercepts at -2, 1, and 5, with the graph touching but not crossing at x=1, and a y-intercept at (0,20). This is the complete equation of the polynomial.
What is f(x) =2(x+2)(x-1)^2(x-5) ?
For the polynomial, f(x)=x^5(x^2+x^4) , this is the total number of complex zeros.
What is 9?
The graph of f(x) is transformed to h(x) by shifting 5 units left and 3 units up. This is the equation of h(x), written as a transformation of f(x).
What is h(x)=f(x+5)+3 ?
A rectangular prism has height (2x+3), width(4x-1), and length (3x+2). This expression represents the surface area of the prism.
What is 2(2x+3)(4x-1)+2(4x-1)(3x+2)+2(3x+2)(2x+3) ?
An author's website visits are V = 50t² - 40t + 200 and book sales are S = 25t + 15, where t is months. After simplifying, this rational expression represents the ratio R of visits to sales.
What is R = (10t^2-8t+40)/(5t+3) ?